Final answer:
It will take the marching band approximately 10 minutes to complete 1 mile.
Step-by-step explanation:
To find the time it will take to complete 1 mile, we can use the given information that the marching band walks 1/15 miles in 2/3 minutes. This is equivalent to a rate of (1/15)/(2/3) miles per minute. To convert this rate to minutes per mile, we can take the reciprocal, which is (2/3)/(1/15) minutes per mile. Simplifying, we find that it will take the marching band approximately 10 minutes to complete 1 mile.